Koopman Spectral Analysis of Lithium-Ion Battery Dynamics: State of Charge as a Marginally Stable Observable

Bakhtiar Nafis, Khalid Mahmud Labib, Saad Waheed, Shabbir Ahmed

Accurate state-of-charge (SOC) estimation remains a fundamental challenge in lithium-ion battery management systems because battery dynamics are highly nonlinear, operating-condition dependent, and sensitive to parameter variations caused by aging and temperature. Conventional model-based estimators, such as equivalent circuit model (ECM) and Kalman-filter-based approaches, rely heavily on repeated parameter identification and accurate electrochemical modeling, whereas purely data-driven methods often sacrifice physical interpretability. This work proposes a Koopman-theoretic, data-driven framework for SOC estimation using Dynamic Mode Decomposition with control (DMDc) combined with Hankel time-delay embedding. Instead of explicitly identifying ECM parameters, the proposed approach reconstructs a lifted dynamical state space directly from measured terminal voltage and current obtained through Hybrid Pulse Power Characterization (HPPC) testing. Spectral decomposition of the identified DMDc operator reveals intrinsic battery dynamics in terms of Koopman modes and eigenvalues. The SOC dynamics naturally emerge as the slowest marginally stable mode whose eigenvalue lies closest to the unit circle, consistent with the integrator-type behavior of charge conservation. The corresponding modal coordinate is subsequently utilized as an SOC-sensitive observable.